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Jiro comments on Just Lose Hope Already - Less Wrong
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In addition, as Eliezer's earlier post about the math proof shows, if the original reason that led you to believe you could do something was shown to be false, you should almost certainly give up. It's very unlikely you were right for the wrong reasons. If, knowing what you know now, you would never have tried, then you should probably stop.
This ignores the case where your "original reason" was an attempt to formalize some informal reason. If your error is in the formalization process and not in the reason itself, being right for the wrong reason is a plausible scenario.